Positive Solutions of a Third-Order Three-Point BVP with Sign-Changing Green’s Function

We are concerned with the following third-order three-point boundary value problem: u ′ ′ ′ t = f t , u t , t ∈ 0 , 1 , u ′ 0 = u 1 = 0 and u ′ ′ η - α u ′ 1 = 0 , where α ∈ 0 , 1 and η ∈ ( 14 + α ) / ( 24 - 3 α ) , 1 . Although the corresponding Green’s function is sign-changing, we still obtain th...

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Published inMathematical problems in engineering Vol. 2014; no. 2014; pp. 1 - 6
Main Authors Gao, Li-Juan, Sun, Jian-Ping
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2014
Hindawi Limited
Subjects
Applied mathematics
Boundary value problems
Existence theorems
Fixed points (mathematics)
Green's functions
Mathematical analysis
Mathematical functions
Mathematical problems
Theorems
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Summary:We are concerned with the following third-order three-point boundary value problem: u ′ ′ ′ t = f t , u t , t ∈ 0 , 1 , u ′ 0 = u 1 = 0 and u ′ ′ η - α u ′ 1 = 0 , where α ∈ 0 , 1 and η ∈ ( 14 + α ) / ( 24 - 3 α ) , 1 . Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson.
Bibliography:ObjectType-Article-1
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ISSN:1024-123X
1563-5147
DOI:10.1155/2014/406815